Category: Limits

Question Number 3460 by prakash jain last updated on 14/Dec/15 $$\mathrm{If}\underset{n=1}{\sum ^{\mathrm{\infty }}}{a}_n\mathrm{is}\mathrm{convergent}\mathrm{and}\underset{n=1}{\sum ^{\mathrm{\infty }}}{b}_n\mathrm{is}\mathrm{convergent}.$$$$\mathrm{What}\mathrm{are}\mathrm{the}\mathrm{sufficient}\mathrm{condition}\mathrm{so}\mathrm{that}$$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} ^{{n}} {b}_{{n}}…

Question Number 68965 by anaplak last updated on 17/Sep/19 Commented by anaplak last updated on 17/Sep/19 $$sirpleasegivemethesolutionshowingbytakingrighthandlimit$$$$imeantosayindetailed$$ Commented by kaivan.ahmadi last…

Question Number 3297 by prakash jain last updated on 09/Dec/15 $$\mathrm{Is}\mathrm{the}\mathrm{following}\mathrm{series}\mathrm{convergent}$$$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{{\left(\ln n\right)}^{\ln \left(\ln n\right)}}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 3138 by prakash jain last updated on 05/Dec/15 $$\mathrm{Prove}\mathrm{or}\mathrm{disprove}\mathrm{that}$$$$\mathrm{S}=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^k},k\in {\mathbb{Z}}^{+},k>1\mathrm{is}\mathrm{irrational}.$$ Commented by 123456 last updated on…

Question Number 134171 by liberty last updated on 28/Feb/21 $$\underset{x\to 0}{\lim }\frac{1+\sin \mathrm{x}-\cos \mathrm{x}}{1+\sin \left(\mathrm{px}\right)-\cos \left(\mathrm{px}\right)}=?$$ Answered by malwan last updated on 28/Feb/21 $$\underset{x\to 0}{lim}\frac{1+(x-\dots )-(1-\dots )}{1+(px-\dots )-(1-\dots )}=\frac{1}{p}$$ Answered…